In the known apparatus of the present invention (DE-AS 12 11 379), the cooling unit for the internal bubble cooling is a cooling water tank with a cylindrical upper part which is adapted to the tubular film bubble and provided with cooling water supply and drain pipes. The cooling attainable in this way is not sufficient in up-to-date units for the production of tubular film and furthermore it is frequently not sufficiently uniform across the circumference of the tubular film bubble. This applies also to a similar type of design (GB-PS 10 72 174) which works with helically guided cooling spirals. By the way, devices of the first described design (DE-AS 12 11 379, GB-PS 10 72 174) are known in which so-called support air is used for inflating the thermo-plasticized plastic tube to a tubular film bubble and only leakage losses are readjusted. However, other devices are known which work with so-called blowing air (DE-OS 23 06 834) and wherein a large mass flow of cooled blowing air is conveyed into the tubular film bubble for internal cooling and an adequate mass flow of air is exhausted out of the tubular film bubble so that cooling is effected by means of the cooled air stream supplied and exhaust is made in a way to allow the tubular film bubble to remain inflated. The obtained cooling effect depends here on the controllability of the mass flows without affecting or even destroying the tubular film bubble.